Exceptional Lie Algebra $E_{7(-25)}$ (Multiplets and Invariant Differential Operators)

Understand

In the present paper we continue the project of systematic construction of invariant differential operators on the example of the non-compact exceptional algebra $E_{7(-25)}$.

• Our choice of this particular algebra is motivated by the fact that it belongs to a narrow class of algebras, which we call 'conformal Lie algebras', which have very similar properties to the conformal algebras of $n$-dimensional Minkowski space-time.
• This class of algebras is identified and summarized in a table.
• Another motivation is related to the AdS/CFT correspondence.